Hearing the Shape of the Ising Model with a Programmable Superconducting-Flux Annealer
Venue
Scientific Reports, vol. 4 (2014)
Publication Year
2014
Authors
Walter Vinci, Klas Markström, Sergio Boixo, Aidan Roy, Federico M. Spedalieri, Paul A. Warburton, Simone Severini
BibTeX
Abstract
Two objects can be distinguished if they have different measurable properties.
Thus, distinguishability depends on the Physics of the objects. In considering
graphs, we revisit the Ising model as a framework to define physically meaningful
spectral invariants. In this context, we introduce a family of refinements of the
classical spectrum and consider the quantum partition function. We demonstrate that
the energy spectrum of the quantum Ising Hamiltonian is a stronger invariant than
the classical one without refinements. For the purpose of implementing the related
physical systems, we perform experiments on a programmable annealer with
superconducting flux technology. Departing from the paradigm of adiabatic
computation, we take advantage of a noisy evolution of the device to generate
statistics of low energy states. The graphs considered in the experiments have the
same classical partition functions, but different quantum spectra. The data
obtained from the annealer distinguish non-isomorphic graphs via information
contained in the classical refinements of the functions but not via the differences
in the quantum spectra.
